Stokes flow

E32707

creeping flow fluid flow regime viscous-dominated flow

Stokes flow is a type of fluid motion dominated by viscous forces and characterized by very low Reynolds numbers, where inertial effects are negligible.

Statements (48)

Predicate	Object
instanceOf	creeping flow → fluid flow regime → viscous-dominated flow →
appliesTo	flow around small particles in a viscous fluid → flow in narrow channels at low speed → motion of microorganisms in viscous environments →
appliesWhen	Reynolds number much less than 1 →
assumes	incompressible fluid in many applications → steady flow in many applications →
characterizedBy	very low Reynolds number →
contrastedWith	high Reynolds number flow → inertial flow → turbulent flow →
fieldOfStudy	continuum mechanics → fluid mechanics →
governedBy	Navier–Stokes equations → surface form: Stokes equations Navier–Stokes equations → surface form: linearized Navier–Stokes equations
hasApproximation	Oseen approximation for slightly higher Reynolds numbers →
hasDimensionlessParameter	Reynolds number →
hasMathematicalForm	∇p = μ∇²u → ∇·u = 0 for incompressible case →
hasProperty	absence of flow separation around obstacles → dominant viscous forces → energy dissipation dominated by viscous effects → laminar flow → linear relationship between forces and velocities → negligible inertial forces → no turbulence → pressure and velocity fields satisfy linear PDEs → reversibility under time reversal in ideal conditions →
hasSolutionType	often solvable by linear superposition →
namedAfter	George Stokes → surface form: George Gabriel Stokes
neglects	nonlinear convective acceleration term in Navier–Stokes equations →
relatedTo	Stokes drag → Stokes law for a sphere →
requires	small characteristic length or velocity or high viscosity →
usedIn	biological fluid dynamics → colloidal science → lubrication theory → microfluidics → porous media flow modeling → rheology of complex fluids → sedimentation analysis → suspension mechanics →
usedToModel	drag on micron-sized particles → slow motion of drops and bubbles in viscous liquids → slow viscous flow in Hele–Shaw cells →
validityCondition	particle Reynolds number much less than 1 →

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Navier–Stokes equations → relatedTo → Stokes flow →